PIGS

문제

Mirko works on a pig farm that consists of M locked pig-houses and Mirko can't unlock any pighouse because he doesn't have the keys. Customers come to the farm one after another. Each of them has keys to some pig-houses and wants to buy a certain number of pigs. 

All data concerning customers planning to visit the farm on that particular day are available to Mirko early in the morning so that he can make a sales-plan in order to maximize the number of pigs sold. 

More precisely, the procedure is as following: the customer arrives, opens all pig-houses to which he has the key, Mirko sells a certain number of pigs from all the unlocked pig-houses to him, and, if Mirko wants, he can redistribute the remaining pigs across the unlocked pig-houses. 

An unlimited number of pigs can be placed in every pig-house. 

Write a program that will find the maximum number of pigs that he can sell on that day.

입력

The first line of input file contains two integers M and N, 1 ≤ M ≤ 1000, 1 ≤ N ≤ 100, number of pighouses and number of customers. Pig houses are numbered from 1 to M and customers are numbered from 1 to N. 

The next line contains M integeres, for each pig-house initial number of pigs. The number of pigs in each pig-house is greater or equal to 0 and less or equal to 1000. 

The next N lines contains records about the customers in the following form ( record about the i-th customer is written in the (i+2)-th line): 

A K₁ K₂ ... K_A B 

It means that this customer has key to the pig-houses marked with the numbers K₁, K₂, ..., K_A (sorted nondecreasingly ) and that he wants to buy B pigs. Numbers A and B can be equal to 0.

출력

The first and only line of the output file should contain the number of sold pigs. 

 

3 3
3 1 10
2 1 2 2 
2 1 3 3
1 2 6

7

6 6
6 3 2 0 1 3
2 1 2 0
1 3 3
1 1 1
2 2 3 8
2 4 5 2
2 4 6 6

15

11 5
1 2 2 1 0 2 4 1 1 1 2
5 1 2 3 4 5 3
4 1 2 6 7 5
2 3 8 1
3 3 6 11 5
3 8 9 10 3

17